There's no good option here. For Parliament to vote to invoke article 50, 500 of 650 MPs would have to vote for something they personally campaigned against, and which they believe to be catastrophically bad for the country.
If they don't vote for it, they are failing to carry out the democratic will of the people. But even then, MPs represent their own constituency (including non-voters), not the voting public across the whole UK, so MPs like Lammy have a strong case that the people in his own constituency have given him a mandate to vote against - not just the 60% or more who voted remain, but the needs of people under 18, and non-UK nationals who didn't get a vote who live in his constituency (a large proportion).
So in all it's hard to see how this could move forward. I wonder if such a vote would ever happen. And if Article 50 will be invoked at all.